Clustering SPH Debris into N-body Fragments: A Collisional Code for Planet Formation

Abstract: Giant impacts among planetary embryos generate long-lived debris that feeds back on late-stage terrestrial planet growth, yet most N-body models either assume perfect merging or treat fragments in ad hoc ways. We present SHARD, a collision-resolution framework that couples a hybrid integrator (REBOUND/mercurius) to a six-dimensional catalog of smoothed-particle hydrodynamics (SPH) outcomes spanning impact speed, geometry, total mass (up to 2 M_earth), mass ratio, and target/projectile water fractions. For each detected impact we multi-linearly interpolate to return the two largest remnants with self-consistent kinematics and volatile budgets, and we reconstruct the unresolved fragment population by aggregating nearby SPH debris snapshots and compressing them with mass-weighted k-means in velocity space into a tractable number of fragments above a tunable minimum mass. Exact conservation of total mass and water mass is enforced across survivors and debris, with immediate, energy-based reaccretion checks performed within the timestep. Debris interpolation is constrained to the tabulated SPH grid (no extrapolation), and special handling of hit-and-run and catastrophic regimes is included. We benchmark our code against SyMBA in a Mercury-formation experiment and find broad qualitative agreement, though our final embryos distribution is dynamically hotter and more top-heavy in mass. The benchmark outcome suggests that debris clustering is dynamically consequential: fragment resolution controls reaccretion, damping, and volatile retention. This SPH-anchored debris treatment provides a drop-in, compositionally aware alternative to perfect merging, enabling late-stage accretion studies that retains fragment feedback without saturating the integrator.